William is 18 years older than Ishaan. For the last 3 years, William and Ishaan have been going to the same school. Nineteen years ago, William was 3 times as old as Ishaan. How old is William now?
Answer: We can use the given information to write down two equations that describe the ages of William and Ishaan. Let William's current age be $w$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $w = i + 18$ Nineteen years ago, William was $w - 19$ years old, and Ishaan was $i - 19$ years old. The information in the second sentence can be expressed in the following equation: $w - 19 = 3(i - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to solve our first equation for $i$ and substitute it into our second equation. Solving our first equation for $i$ , we get: $i = w - 18$ . Substituting this into our second equation, we get the equation: $w - 19 = 3($ $(w - 18)$ $ -$ $ 19)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $w - 19 = 3w - 111$ Solving for $w$ , we get: $2 w = 92$ $w = 46$.